The short memory principle for solving Abel differential equation of fractional order. (English) Zbl 1236.34008

Summary: The short memory principle (SMP) is applied for solving the Abel differential equation with fractional order. We evaluate the approximate solution at the end of required interval, and construct a suitable iteration scheme employing this end point as initial value. Numerical experiments show that our iteration method is simple and efficient, and that a proper length of memory could maintain the validity of the short memory principle.


34A08 Fractional ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
45J05 Integro-ordinary differential equations
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